Negotiating salary: am I doing it right?

Hi there r/jobs. I've been searching for a job for the past 5 months but I finally got offered two! I have accepted the offer for one but it is at-will so I can leave if need be for the other. I have not received an official offer from the other. I like them both about the same (#2 a little more than #1), but #2 just happened to come right after I accepted #1. I plan on negotiating salary with #2 by seeing if they can match #1's because the reason why I was so quick to jump on #1 is because they salary is pretty generous as well as the career trajectory. #2 has a more questionable career trajectory at that company but would overall provide solid career experience. My question basically boils down to this: should I open a negotiation as mentioned above i.e. "can you match this?"